Confronting Spectral Functions from e+e− Annihilation and τ Decays: Consequences for the Muon Magnetic Moment

Vacuum polarization integrals involve the vector spectral functions which can be experimentally determined from two sources: (i) ee annihilation cross sections and (ii) hadronic τ decays. Recently results with comparable precision have become available from CMD-2 on one side, and ALEPH, CLEO and OPAL on the other. The comparison of the respective spectral functions involves a correction from isospin-breaking effects, which is evaluated. After the correction it is found that the dominant ππ spectral functions do not agree within experimental and theoretical uncertainties. Some disagreement is also found for the 4π spectral functions. The consequences of these discrepancies for vacuum polarization calculations are presented, with the emphasis on the muon anomalous magnetic moment. Adding quadratically experimental and theoretical uncertainties, we find that the full Standard Model prediction of aμ deviates from the recent BNL measurement at the level of 3.0 (e + e −-based) and 0.9 (τ -based) standard deviations.